A continuous-time signal xc(t) is bandlimited such that xc(jω) = 0 for ǀωǀ ≥ 2π(1000). Thi...

A continuous-time signal xc(t) is bandlimited such that xc(jω) = 0 for ǀωǀ ≥ 2π(1000). This signal is sampled with sampling rate fs = 1/Ts producing the sequence x[n] = xc(nTs) as in Fig. 1. Assume that the window is a rectangular window whose length L is equal to the DFT length, N. Furthermore, for efficiency in computation, assume that N is a power of two. Both fs and N can be chosen at will subject to the constraints that aliasing be avoided and N = 2V. Determine the minimum value of N and the range of sampling rates fsmin< fs<fsmax so that the effective spacing between DFT frequencies is less than or equal to 5 Hz. Give numerical values for N, fsmin and fsmax.

Figure 1 Discrete-time spectrum analysis using time domain windowing and the DFT. The window w[n] should be a finite-length sequence.